src/HOL/Library/Old_Datatype.thy
author wenzelm
Sun Nov 02 17:20:45 2014 +0100 (2014-11-02)
changeset 58881 b9556a055632
parent 58390 b74d8470b98e
child 60500 903bb1495239
permissions -rw-r--r--
modernized header;
     1 (*  Title:      HOL/Library/Old_Datatype.thy
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen
     4 *)
     5 
     6 section {* Old Datatype package: constructing datatypes from Cartesian Products and Disjoint Sums *}
     7 
     8 theory Old_Datatype
     9 imports "../Main"
    10 keywords "old_datatype" :: thy_decl
    11 begin
    12 
    13 ML_file "~~/src/HOL/Tools/datatype_realizer.ML"
    14 
    15 
    16 subsection {* The datatype universe *}
    17 
    18 definition "Node = {p. EX f x k. p = (f :: nat => 'b + nat, x ::'a + nat) & f k = Inr 0}"
    19 
    20 typedef ('a, 'b) node = "Node :: ((nat => 'b + nat) * ('a + nat)) set"
    21   morphisms Rep_Node Abs_Node
    22   unfolding Node_def by auto
    23 
    24 text{*Datatypes will be represented by sets of type @{text node}*}
    25 
    26 type_synonym 'a item        = "('a, unit) node set"
    27 type_synonym ('a, 'b) dtree = "('a, 'b) node set"
    28 
    29 consts
    30   Push      :: "[('b + nat), nat => ('b + nat)] => (nat => ('b + nat))"
    31 
    32   Push_Node :: "[('b + nat), ('a, 'b) node] => ('a, 'b) node"
    33   ndepth    :: "('a, 'b) node => nat"
    34 
    35   Atom      :: "('a + nat) => ('a, 'b) dtree"
    36   Leaf      :: "'a => ('a, 'b) dtree"
    37   Numb      :: "nat => ('a, 'b) dtree"
    38   Scons     :: "[('a, 'b) dtree, ('a, 'b) dtree] => ('a, 'b) dtree"
    39   In0       :: "('a, 'b) dtree => ('a, 'b) dtree"
    40   In1       :: "('a, 'b) dtree => ('a, 'b) dtree"
    41   Lim       :: "('b => ('a, 'b) dtree) => ('a, 'b) dtree"
    42 
    43   ntrunc    :: "[nat, ('a, 'b) dtree] => ('a, 'b) dtree"
    44 
    45   uprod     :: "[('a, 'b) dtree set, ('a, 'b) dtree set]=> ('a, 'b) dtree set"
    46   usum      :: "[('a, 'b) dtree set, ('a, 'b) dtree set]=> ('a, 'b) dtree set"
    47 
    48   Split     :: "[[('a, 'b) dtree, ('a, 'b) dtree]=>'c, ('a, 'b) dtree] => 'c"
    49   Case      :: "[[('a, 'b) dtree]=>'c, [('a, 'b) dtree]=>'c, ('a, 'b) dtree] => 'c"
    50 
    51   dprod     :: "[(('a, 'b) dtree * ('a, 'b) dtree)set, (('a, 'b) dtree * ('a, 'b) dtree)set]
    52                 => (('a, 'b) dtree * ('a, 'b) dtree)set"
    53   dsum      :: "[(('a, 'b) dtree * ('a, 'b) dtree)set, (('a, 'b) dtree * ('a, 'b) dtree)set]
    54                 => (('a, 'b) dtree * ('a, 'b) dtree)set"
    55 
    56 
    57 defs
    58 
    59   Push_Node_def:  "Push_Node == (%n x. Abs_Node (apfst (Push n) (Rep_Node x)))"
    60 
    61   (*crude "lists" of nats -- needed for the constructions*)
    62   Push_def:   "Push == (%b h. case_nat b h)"
    63 
    64   (** operations on S-expressions -- sets of nodes **)
    65 
    66   (*S-expression constructors*)
    67   Atom_def:   "Atom == (%x. {Abs_Node((%k. Inr 0, x))})"
    68   Scons_def:  "Scons M N == (Push_Node (Inr 1) ` M) Un (Push_Node (Inr (Suc 1)) ` N)"
    69 
    70   (*Leaf nodes, with arbitrary or nat labels*)
    71   Leaf_def:   "Leaf == Atom o Inl"
    72   Numb_def:   "Numb == Atom o Inr"
    73 
    74   (*Injections of the "disjoint sum"*)
    75   In0_def:    "In0(M) == Scons (Numb 0) M"
    76   In1_def:    "In1(M) == Scons (Numb 1) M"
    77 
    78   (*Function spaces*)
    79   Lim_def: "Lim f == Union {z. ? x. z = Push_Node (Inl x) ` (f x)}"
    80 
    81   (*the set of nodes with depth less than k*)
    82   ndepth_def: "ndepth(n) == (%(f,x). LEAST k. f k = Inr 0) (Rep_Node n)"
    83   ntrunc_def: "ntrunc k N == {n. n:N & ndepth(n)<k}"
    84 
    85   (*products and sums for the "universe"*)
    86   uprod_def:  "uprod A B == UN x:A. UN y:B. { Scons x y }"
    87   usum_def:   "usum A B == In0`A Un In1`B"
    88 
    89   (*the corresponding eliminators*)
    90   Split_def:  "Split c M == THE u. EX x y. M = Scons x y & u = c x y"
    91 
    92   Case_def:   "Case c d M == THE u.  (EX x . M = In0(x) & u = c(x))
    93                                   | (EX y . M = In1(y) & u = d(y))"
    94 
    95 
    96   (** equality for the "universe" **)
    97 
    98   dprod_def:  "dprod r s == UN (x,x'):r. UN (y,y'):s. {(Scons x y, Scons x' y')}"
    99 
   100   dsum_def:   "dsum r s == (UN (x,x'):r. {(In0(x),In0(x'))}) Un
   101                           (UN (y,y'):s. {(In1(y),In1(y'))})"
   102 
   103 
   104 
   105 lemma apfst_convE: 
   106     "[| q = apfst f p;  !!x y. [| p = (x,y);  q = (f(x),y) |] ==> R  
   107      |] ==> R"
   108 by (force simp add: apfst_def)
   109 
   110 (** Push -- an injection, analogous to Cons on lists **)
   111 
   112 lemma Push_inject1: "Push i f = Push j g  ==> i=j"
   113 apply (simp add: Push_def fun_eq_iff) 
   114 apply (drule_tac x=0 in spec, simp) 
   115 done
   116 
   117 lemma Push_inject2: "Push i f = Push j g  ==> f=g"
   118 apply (auto simp add: Push_def fun_eq_iff) 
   119 apply (drule_tac x="Suc x" in spec, simp) 
   120 done
   121 
   122 lemma Push_inject:
   123     "[| Push i f =Push j g;  [| i=j;  f=g |] ==> P |] ==> P"
   124 by (blast dest: Push_inject1 Push_inject2) 
   125 
   126 lemma Push_neq_K0: "Push (Inr (Suc k)) f = (%z. Inr 0) ==> P"
   127 by (auto simp add: Push_def fun_eq_iff split: nat.split_asm)
   128 
   129 lemmas Abs_Node_inj = Abs_Node_inject [THEN [2] rev_iffD1]
   130 
   131 
   132 (*** Introduction rules for Node ***)
   133 
   134 lemma Node_K0_I: "(%k. Inr 0, a) : Node"
   135 by (simp add: Node_def)
   136 
   137 lemma Node_Push_I: "p: Node ==> apfst (Push i) p : Node"
   138 apply (simp add: Node_def Push_def) 
   139 apply (fast intro!: apfst_conv nat.case(2)[THEN trans])
   140 done
   141 
   142 
   143 subsection{*Freeness: Distinctness of Constructors*}
   144 
   145 (** Scons vs Atom **)
   146 
   147 lemma Scons_not_Atom [iff]: "Scons M N \<noteq> Atom(a)"
   148 unfolding Atom_def Scons_def Push_Node_def One_nat_def
   149 by (blast intro: Node_K0_I Rep_Node [THEN Node_Push_I] 
   150          dest!: Abs_Node_inj 
   151          elim!: apfst_convE sym [THEN Push_neq_K0])  
   152 
   153 lemmas Atom_not_Scons [iff] = Scons_not_Atom [THEN not_sym]
   154 
   155 
   156 (*** Injectiveness ***)
   157 
   158 (** Atomic nodes **)
   159 
   160 lemma inj_Atom: "inj(Atom)"
   161 apply (simp add: Atom_def)
   162 apply (blast intro!: inj_onI Node_K0_I dest!: Abs_Node_inj)
   163 done
   164 lemmas Atom_inject = inj_Atom [THEN injD]
   165 
   166 lemma Atom_Atom_eq [iff]: "(Atom(a)=Atom(b)) = (a=b)"
   167 by (blast dest!: Atom_inject)
   168 
   169 lemma inj_Leaf: "inj(Leaf)"
   170 apply (simp add: Leaf_def o_def)
   171 apply (rule inj_onI)
   172 apply (erule Atom_inject [THEN Inl_inject])
   173 done
   174 
   175 lemmas Leaf_inject [dest!] = inj_Leaf [THEN injD]
   176 
   177 lemma inj_Numb: "inj(Numb)"
   178 apply (simp add: Numb_def o_def)
   179 apply (rule inj_onI)
   180 apply (erule Atom_inject [THEN Inr_inject])
   181 done
   182 
   183 lemmas Numb_inject [dest!] = inj_Numb [THEN injD]
   184 
   185 
   186 (** Injectiveness of Push_Node **)
   187 
   188 lemma Push_Node_inject:
   189     "[| Push_Node i m =Push_Node j n;  [| i=j;  m=n |] ==> P  
   190      |] ==> P"
   191 apply (simp add: Push_Node_def)
   192 apply (erule Abs_Node_inj [THEN apfst_convE])
   193 apply (rule Rep_Node [THEN Node_Push_I])+
   194 apply (erule sym [THEN apfst_convE]) 
   195 apply (blast intro: Rep_Node_inject [THEN iffD1] trans sym elim!: Push_inject)
   196 done
   197 
   198 
   199 (** Injectiveness of Scons **)
   200 
   201 lemma Scons_inject_lemma1: "Scons M N <= Scons M' N' ==> M<=M'"
   202 unfolding Scons_def One_nat_def
   203 by (blast dest!: Push_Node_inject)
   204 
   205 lemma Scons_inject_lemma2: "Scons M N <= Scons M' N' ==> N<=N'"
   206 unfolding Scons_def One_nat_def
   207 by (blast dest!: Push_Node_inject)
   208 
   209 lemma Scons_inject1: "Scons M N = Scons M' N' ==> M=M'"
   210 apply (erule equalityE)
   211 apply (iprover intro: equalityI Scons_inject_lemma1)
   212 done
   213 
   214 lemma Scons_inject2: "Scons M N = Scons M' N' ==> N=N'"
   215 apply (erule equalityE)
   216 apply (iprover intro: equalityI Scons_inject_lemma2)
   217 done
   218 
   219 lemma Scons_inject:
   220     "[| Scons M N = Scons M' N';  [| M=M';  N=N' |] ==> P |] ==> P"
   221 by (iprover dest: Scons_inject1 Scons_inject2)
   222 
   223 lemma Scons_Scons_eq [iff]: "(Scons M N = Scons M' N') = (M=M' & N=N')"
   224 by (blast elim!: Scons_inject)
   225 
   226 (*** Distinctness involving Leaf and Numb ***)
   227 
   228 (** Scons vs Leaf **)
   229 
   230 lemma Scons_not_Leaf [iff]: "Scons M N \<noteq> Leaf(a)"
   231 unfolding Leaf_def o_def by (rule Scons_not_Atom)
   232 
   233 lemmas Leaf_not_Scons  [iff] = Scons_not_Leaf [THEN not_sym]
   234 
   235 (** Scons vs Numb **)
   236 
   237 lemma Scons_not_Numb [iff]: "Scons M N \<noteq> Numb(k)"
   238 unfolding Numb_def o_def by (rule Scons_not_Atom)
   239 
   240 lemmas Numb_not_Scons [iff] = Scons_not_Numb [THEN not_sym]
   241 
   242 
   243 (** Leaf vs Numb **)
   244 
   245 lemma Leaf_not_Numb [iff]: "Leaf(a) \<noteq> Numb(k)"
   246 by (simp add: Leaf_def Numb_def)
   247 
   248 lemmas Numb_not_Leaf [iff] = Leaf_not_Numb [THEN not_sym]
   249 
   250 
   251 (*** ndepth -- the depth of a node ***)
   252 
   253 lemma ndepth_K0: "ndepth (Abs_Node(%k. Inr 0, x)) = 0"
   254 by (simp add: ndepth_def  Node_K0_I [THEN Abs_Node_inverse] Least_equality)
   255 
   256 lemma ndepth_Push_Node_aux:
   257      "case_nat (Inr (Suc i)) f k = Inr 0 --> Suc(LEAST x. f x = Inr 0) <= k"
   258 apply (induct_tac "k", auto)
   259 apply (erule Least_le)
   260 done
   261 
   262 lemma ndepth_Push_Node: 
   263     "ndepth (Push_Node (Inr (Suc i)) n) = Suc(ndepth(n))"
   264 apply (insert Rep_Node [of n, unfolded Node_def])
   265 apply (auto simp add: ndepth_def Push_Node_def
   266                  Rep_Node [THEN Node_Push_I, THEN Abs_Node_inverse])
   267 apply (rule Least_equality)
   268 apply (auto simp add: Push_def ndepth_Push_Node_aux)
   269 apply (erule LeastI)
   270 done
   271 
   272 
   273 (*** ntrunc applied to the various node sets ***)
   274 
   275 lemma ntrunc_0 [simp]: "ntrunc 0 M = {}"
   276 by (simp add: ntrunc_def)
   277 
   278 lemma ntrunc_Atom [simp]: "ntrunc (Suc k) (Atom a) = Atom(a)"
   279 by (auto simp add: Atom_def ntrunc_def ndepth_K0)
   280 
   281 lemma ntrunc_Leaf [simp]: "ntrunc (Suc k) (Leaf a) = Leaf(a)"
   282 unfolding Leaf_def o_def by (rule ntrunc_Atom)
   283 
   284 lemma ntrunc_Numb [simp]: "ntrunc (Suc k) (Numb i) = Numb(i)"
   285 unfolding Numb_def o_def by (rule ntrunc_Atom)
   286 
   287 lemma ntrunc_Scons [simp]: 
   288     "ntrunc (Suc k) (Scons M N) = Scons (ntrunc k M) (ntrunc k N)"
   289 unfolding Scons_def ntrunc_def One_nat_def
   290 by (auto simp add: ndepth_Push_Node)
   291 
   292 
   293 
   294 (** Injection nodes **)
   295 
   296 lemma ntrunc_one_In0 [simp]: "ntrunc (Suc 0) (In0 M) = {}"
   297 apply (simp add: In0_def)
   298 apply (simp add: Scons_def)
   299 done
   300 
   301 lemma ntrunc_In0 [simp]: "ntrunc (Suc(Suc k)) (In0 M) = In0 (ntrunc (Suc k) M)"
   302 by (simp add: In0_def)
   303 
   304 lemma ntrunc_one_In1 [simp]: "ntrunc (Suc 0) (In1 M) = {}"
   305 apply (simp add: In1_def)
   306 apply (simp add: Scons_def)
   307 done
   308 
   309 lemma ntrunc_In1 [simp]: "ntrunc (Suc(Suc k)) (In1 M) = In1 (ntrunc (Suc k) M)"
   310 by (simp add: In1_def)
   311 
   312 
   313 subsection{*Set Constructions*}
   314 
   315 
   316 (*** Cartesian Product ***)
   317 
   318 lemma uprodI [intro!]: "[| M:A;  N:B |] ==> Scons M N : uprod A B"
   319 by (simp add: uprod_def)
   320 
   321 (*The general elimination rule*)
   322 lemma uprodE [elim!]:
   323     "[| c : uprod A B;   
   324         !!x y. [| x:A;  y:B;  c = Scons x y |] ==> P  
   325      |] ==> P"
   326 by (auto simp add: uprod_def) 
   327 
   328 
   329 (*Elimination of a pair -- introduces no eigenvariables*)
   330 lemma uprodE2: "[| Scons M N : uprod A B;  [| M:A;  N:B |] ==> P |] ==> P"
   331 by (auto simp add: uprod_def)
   332 
   333 
   334 (*** Disjoint Sum ***)
   335 
   336 lemma usum_In0I [intro]: "M:A ==> In0(M) : usum A B"
   337 by (simp add: usum_def)
   338 
   339 lemma usum_In1I [intro]: "N:B ==> In1(N) : usum A B"
   340 by (simp add: usum_def)
   341 
   342 lemma usumE [elim!]: 
   343     "[| u : usum A B;   
   344         !!x. [| x:A;  u=In0(x) |] ==> P;  
   345         !!y. [| y:B;  u=In1(y) |] ==> P  
   346      |] ==> P"
   347 by (auto simp add: usum_def)
   348 
   349 
   350 (** Injection **)
   351 
   352 lemma In0_not_In1 [iff]: "In0(M) \<noteq> In1(N)"
   353 unfolding In0_def In1_def One_nat_def by auto
   354 
   355 lemmas In1_not_In0 [iff] = In0_not_In1 [THEN not_sym]
   356 
   357 lemma In0_inject: "In0(M) = In0(N) ==>  M=N"
   358 by (simp add: In0_def)
   359 
   360 lemma In1_inject: "In1(M) = In1(N) ==>  M=N"
   361 by (simp add: In1_def)
   362 
   363 lemma In0_eq [iff]: "(In0 M = In0 N) = (M=N)"
   364 by (blast dest!: In0_inject)
   365 
   366 lemma In1_eq [iff]: "(In1 M = In1 N) = (M=N)"
   367 by (blast dest!: In1_inject)
   368 
   369 lemma inj_In0: "inj In0"
   370 by (blast intro!: inj_onI)
   371 
   372 lemma inj_In1: "inj In1"
   373 by (blast intro!: inj_onI)
   374 
   375 
   376 (*** Function spaces ***)
   377 
   378 lemma Lim_inject: "Lim f = Lim g ==> f = g"
   379 apply (simp add: Lim_def)
   380 apply (rule ext)
   381 apply (blast elim!: Push_Node_inject)
   382 done
   383 
   384 
   385 (*** proving equality of sets and functions using ntrunc ***)
   386 
   387 lemma ntrunc_subsetI: "ntrunc k M <= M"
   388 by (auto simp add: ntrunc_def)
   389 
   390 lemma ntrunc_subsetD: "(!!k. ntrunc k M <= N) ==> M<=N"
   391 by (auto simp add: ntrunc_def)
   392 
   393 (*A generalized form of the take-lemma*)
   394 lemma ntrunc_equality: "(!!k. ntrunc k M = ntrunc k N) ==> M=N"
   395 apply (rule equalityI)
   396 apply (rule_tac [!] ntrunc_subsetD)
   397 apply (rule_tac [!] ntrunc_subsetI [THEN [2] subset_trans], auto) 
   398 done
   399 
   400 lemma ntrunc_o_equality: 
   401     "[| !!k. (ntrunc(k) o h1) = (ntrunc(k) o h2) |] ==> h1=h2"
   402 apply (rule ntrunc_equality [THEN ext])
   403 apply (simp add: fun_eq_iff) 
   404 done
   405 
   406 
   407 (*** Monotonicity ***)
   408 
   409 lemma uprod_mono: "[| A<=A';  B<=B' |] ==> uprod A B <= uprod A' B'"
   410 by (simp add: uprod_def, blast)
   411 
   412 lemma usum_mono: "[| A<=A';  B<=B' |] ==> usum A B <= usum A' B'"
   413 by (simp add: usum_def, blast)
   414 
   415 lemma Scons_mono: "[| M<=M';  N<=N' |] ==> Scons M N <= Scons M' N'"
   416 by (simp add: Scons_def, blast)
   417 
   418 lemma In0_mono: "M<=N ==> In0(M) <= In0(N)"
   419 by (simp add: In0_def Scons_mono)
   420 
   421 lemma In1_mono: "M<=N ==> In1(M) <= In1(N)"
   422 by (simp add: In1_def Scons_mono)
   423 
   424 
   425 (*** Split and Case ***)
   426 
   427 lemma Split [simp]: "Split c (Scons M N) = c M N"
   428 by (simp add: Split_def)
   429 
   430 lemma Case_In0 [simp]: "Case c d (In0 M) = c(M)"
   431 by (simp add: Case_def)
   432 
   433 lemma Case_In1 [simp]: "Case c d (In1 N) = d(N)"
   434 by (simp add: Case_def)
   435 
   436 
   437 
   438 (**** UN x. B(x) rules ****)
   439 
   440 lemma ntrunc_UN1: "ntrunc k (UN x. f(x)) = (UN x. ntrunc k (f x))"
   441 by (simp add: ntrunc_def, blast)
   442 
   443 lemma Scons_UN1_x: "Scons (UN x. f x) M = (UN x. Scons (f x) M)"
   444 by (simp add: Scons_def, blast)
   445 
   446 lemma Scons_UN1_y: "Scons M (UN x. f x) = (UN x. Scons M (f x))"
   447 by (simp add: Scons_def, blast)
   448 
   449 lemma In0_UN1: "In0(UN x. f(x)) = (UN x. In0(f(x)))"
   450 by (simp add: In0_def Scons_UN1_y)
   451 
   452 lemma In1_UN1: "In1(UN x. f(x)) = (UN x. In1(f(x)))"
   453 by (simp add: In1_def Scons_UN1_y)
   454 
   455 
   456 (*** Equality for Cartesian Product ***)
   457 
   458 lemma dprodI [intro!]: 
   459     "[| (M,M'):r;  (N,N'):s |] ==> (Scons M N, Scons M' N') : dprod r s"
   460 by (auto simp add: dprod_def)
   461 
   462 (*The general elimination rule*)
   463 lemma dprodE [elim!]: 
   464     "[| c : dprod r s;   
   465         !!x y x' y'. [| (x,x') : r;  (y,y') : s;  
   466                         c = (Scons x y, Scons x' y') |] ==> P  
   467      |] ==> P"
   468 by (auto simp add: dprod_def)
   469 
   470 
   471 (*** Equality for Disjoint Sum ***)
   472 
   473 lemma dsum_In0I [intro]: "(M,M'):r ==> (In0(M), In0(M')) : dsum r s"
   474 by (auto simp add: dsum_def)
   475 
   476 lemma dsum_In1I [intro]: "(N,N'):s ==> (In1(N), In1(N')) : dsum r s"
   477 by (auto simp add: dsum_def)
   478 
   479 lemma dsumE [elim!]: 
   480     "[| w : dsum r s;   
   481         !!x x'. [| (x,x') : r;  w = (In0(x), In0(x')) |] ==> P;  
   482         !!y y'. [| (y,y') : s;  w = (In1(y), In1(y')) |] ==> P  
   483      |] ==> P"
   484 by (auto simp add: dsum_def)
   485 
   486 
   487 (*** Monotonicity ***)
   488 
   489 lemma dprod_mono: "[| r<=r';  s<=s' |] ==> dprod r s <= dprod r' s'"
   490 by blast
   491 
   492 lemma dsum_mono: "[| r<=r';  s<=s' |] ==> dsum r s <= dsum r' s'"
   493 by blast
   494 
   495 
   496 (*** Bounding theorems ***)
   497 
   498 lemma dprod_Sigma: "(dprod (A <*> B) (C <*> D)) <= (uprod A C) <*> (uprod B D)"
   499 by blast
   500 
   501 lemmas dprod_subset_Sigma = subset_trans [OF dprod_mono dprod_Sigma]
   502 
   503 (*Dependent version*)
   504 lemma dprod_subset_Sigma2:
   505     "(dprod (Sigma A B) (Sigma C D)) <= Sigma (uprod A C) (Split (%x y. uprod (B x) (D y)))"
   506 by auto
   507 
   508 lemma dsum_Sigma: "(dsum (A <*> B) (C <*> D)) <= (usum A C) <*> (usum B D)"
   509 by blast
   510 
   511 lemmas dsum_subset_Sigma = subset_trans [OF dsum_mono dsum_Sigma]
   512 
   513 
   514 (*** Domain theorems ***)
   515 
   516 lemma Domain_dprod [simp]: "Domain (dprod r s) = uprod (Domain r) (Domain s)"
   517   by auto
   518 
   519 lemma Domain_dsum [simp]: "Domain (dsum r s) = usum (Domain r) (Domain s)"
   520   by auto
   521 
   522 
   523 text {* hides popular names *}
   524 hide_type (open) node item
   525 hide_const (open) Push Node Atom Leaf Numb Lim Split Case
   526 
   527 ML_file "~~/src/HOL/Tools/Old_Datatype/old_datatype.ML"
   528 ML_file "~~/src/HOL/Tools/inductive_realizer.ML"
   529 
   530 end